Egor Sukhov
Volokolamskoe sh. 4, GSP3, A80, Moscow, 125993 Russia
Moscow aviation institute (National Research University)
Publications:
Bardin B. S., Sukhov E. A., Volkov E. V.
Nonlinear Orbital Stability of Periodic Motions in the Planar Restricted FourBody Problem
2023, Vol. 19, no. 4, pp. 545557
Abstract
We consider the planar circular restricted fourbody problem with a small body of negligible
mass moving in the Newtonian gravitational field of three primary bodies, which form a stable
Lagrangian triangle. The small body moves in the same plane with the primaries. We assume
that two of the primaries have equal masses. In this case the small body has three relative
equilibrium positions located on the central bisector of the Lagrangian triangle. In this work we study the nonlinear orbital stability problem for periodic motions emanating from the stable relative equilibrium. To describe motions of the small body in a neighborhood of its periodic orbit, we introduce the socalled local variables. Then we reduce the orbital stability problem to the stability problem of a stationary point of symplectic mapping generated by the system phase flow on the energy level corresponding to the unperturbed periodic motion. This allows rigorous conclusions to be drawn on orbital stability for both the nonresonant and the resonant cases. We apply this method to investigate orbital stability in the case of third and fourthorder resonances as well as in the nonresonant case. The results of the study are presented in the form of a stability diagram. 
Sukhov E. A., Volkov E. V.
Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted FourBody Problem
2022, Vol. 18, no. 4, pp. 563576
Abstract
We address the planar restricted fourbody problem with a small body of negligible mass
moving in the Newtonian gravitational field of three primary bodies with nonnegligible masses.
We assume that two of the primaries have equal masses and that all primary bodies move in
circular orbits forming a Lagrangian equilateral triangular configuration. This configuration
admits relative equilibria for the small body analogous to the libration points in the threebody
problem. We consider the equilibrium points located on the perpendicular bisector of
the Lagrangian triangle in which case the bodies constitute the socalled central configurations.
Using the method of normal forms, we analytically obtain families of periodic motions emanating
from the stable relative equilibria in a nonresonant case and continue them numerically to the
borders of their existence domains. Using a numerical method, we investigate the orbital stability
of the aforementioned periodic motions and represent the conclusions as stability diagrams in
the problemâ€™s parameter space.

Sukhov E. A.
Bifurcation Analysis of Periodic Motions Originating from Regular Precessions of a Dynamically Symmetric Satellite
2019, Vol. 15, no. 4, pp. 593609
Abstract
We deal with motions of a dynamically symmetric rigidbody satellite about its center of mass in a central Newtonian gravitational field. In this case the equations of motion possess particular solutions representing the socalled regular precessions: cylindrical, conical and hyperboloidal precession. If a regular precession is stable there exist two types of periodic motions in its neighborhood: shortperiodic motions with a period close to $2\pi / \omega_2$ and longperiodic motions with a~period close to $2 \pi / \omega_1$ where $\omega_2$ and $\omega_1$ are the frequencies of the linearized system ($\omega_2 > \omega_1$). In this work we obtain analytically and numerically families of shortperiodic motions arising from regular precessions of a symmetric satellite in a nonresonant case and longperiodic motions arising from hyperboloidal precession in cases of third and fourthorder resonances. We investigate the bifurcation problem for these families of periodic motions and present the results in the form of bifurcation diagrams and Poincaré maps. 